{"id":"https://openalex.org/W1986460515","doi":"https://doi.org/10.1137/060678555","title":"Localized Linear Polynomial Operators and Quadrature Formulas on the Sphere","display_name":"Localized Linear Polynomial Operators and Quadrature Formulas on the Sphere","publication_year":2008,"publication_date":"2008-12-05","ids":{"openalex":"https://openalex.org/W1986460515","doi":"https://doi.org/10.1137/060678555","mag":"1986460515"},"language":"en","primary_location":{"id":"doi:10.1137/060678555","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060678555","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0811.1374","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Q. T. Le Gia","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Q. T. Le Gia","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"H. N. Mhaskar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. N. Mhaskar","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6151,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.87924419,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"47","issue":"1","first_page":"440","last_page":"466"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.6100999712944031,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.6100999712944031,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.06279999762773514,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.03180000185966492,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.611299991607666},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5149000287055969},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4049000144004822},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.40310001373291016},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.3968000113964081},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.3937999904155731},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.3747999966144562},{"id":"https://openalex.org/keywords/gauss\u2013kronrod-quadrature-formula","display_name":"Gauss\u2013Kronrod quadrature formula","score":0.36649999022483826},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.32330000400543213}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8654000163078308},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.611299991607666},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5149000287055969},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43220001459121704},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4049000144004822},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.3968000113964081},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3937999904155731},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3747999966144562},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.36649999022483826},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36399999260902405},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.32330000400543213},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.3089999854564667},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3082999885082245},{"id":"https://openalex.org/C172657837","wikidata":"https://www.wikidata.org/wiki/Q5131618","display_name":"Clenshaw\u2013Curtis quadrature","level":5,"score":0.3077000081539154},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29089999198913574},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.2775999903678894},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.2669999897480011},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.2558000087738037},{"id":"https://openalex.org/C137665795","wikidata":"https://www.wikidata.org/wiki/Q7576710","display_name":"Spherical mean","level":2,"score":0.2529999911785126}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060678555","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060678555","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0811.1374","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0811.1374","pdf_url":"https://arxiv.org/pdf/0811.1374","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0811.1374","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0811.1374","pdf_url":"https://arxiv.org/pdf/0811.1374","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W193027599","https://openalex.org/W319411128","https://openalex.org/W1967265832","https://openalex.org/W1978798278","https://openalex.org/W1981867435","https://openalex.org/W1998258828","https://openalex.org/W2000374238","https://openalex.org/W2002337104","https://openalex.org/W2014992345","https://openalex.org/W2053888374","https://openalex.org/W2063945997","https://openalex.org/W2080261710","https://openalex.org/W2087255259","https://openalex.org/W2094162145","https://openalex.org/W2109735848","https://openalex.org/W2160615084"],"related_works":[],"abstract_inverted_index":{"The":[0,25],"purpose":[1],"of":[2,30,70,82,109,131,146],"this":[3],"paper":[4],"is":[5,67],"to":[6,47,96,120,139],"construct":[7,121,140],"universal,":[8],"auto-adaptive,":[9],"localized,":[10],"linear,":[11],"polynomial":[12,59],"(-valued)":[13],"operators":[14,32],"based":[15,73,89],"on":[16,19,74,90],"scattered":[17,75,91],"data":[18],"the":[20,68,107,110,117],"(hyper)":[21],"sphere":[22],"$\\mathbb{S}^q$":[23],"($q\\ge2$).":[24],"approximation":[26],"and":[27,55],"localization":[28],"properties":[29],"our":[31,65],"are":[33,45,88,137],"studied":[34],"theoretically":[35],"in":[36,64,94,112],"deterministic":[37],"as":[38,40,100],"well":[39],"probabilistic":[41],"settings.":[42],"Numerical":[43],"experiments":[44],"presented":[46],"demonstrate":[48],"their":[49],"superiority":[50],"over":[51],"traditional":[52],"least":[53],"squares":[54],"discrete":[56],"Fourier":[57],"projection":[58],"approximations.":[60],"An":[61],"essential":[62],"ingredient":[63],"construction":[66,69],"quadrature":[71],"formulas":[72,87,99,123,126,141],"data,":[76],"exact":[77,127,142],"for":[78,128,143],"integrating":[79],"spherical":[80,129,144],"polynomials":[81,130,145],"(moderately)":[83],"high":[84],"degree.":[85],"Our":[86],"sites;":[92],"i.e.,":[93],"contrast":[95],"such":[97,122],"well-known":[98],"Driscoll\u2013Healy":[101],"formulas,":[102],"we":[103,136],"need":[104],"not":[105],"choose":[106],"location":[108],"sites":[111],"any":[113],"particular":[114],"manner.":[115],"While":[116],"previous":[118],"attempts":[119],"have":[124],"yielded":[125],"degree":[132,147],"at":[133],"most":[134],"18,":[135],"able":[138],"178.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}